A yarmulke is worn for indoor use when one would normally be bareheaded (for a goy). They are not very good as outdoor hats since they blow away. An outdoor hat is usually needed. Some people put the outdoor over the yarmulke, others put the yarmulke in the pocket while wearing an outdoor hat.
Baseball caps are a popular style of outdoor non-dress hats. One would not wear a baseball hat at a formal event. Other non-dress hats currently popular include a wide variety of caps. Among all Americans, baseball caps are quite popular.
I have never seen anyone wearing a baseball hat to shul on Shabbos.